By Monday morning, when the Post cover showing Mr. Weiner and his son, Jordan, hit newsstands, Mr. Weiner had left the Hamptons for New York City aware that Ms. Abedin planned to announce their separation, said two people close to the couple who discussed private conversations on the condition of anonymity.

“After long and painful consideration and work on my marriage, I have made the decision to separate from my husband,” Ms. Abedin said in a statement. “Anthony and I remain devoted to doing what is best for our son, who is the light of our life. During this difficult time, I ask for respect for our privacy.”

In the latest issue of Vogue, Ms. Abedin portrayed Mr. Weiner as a devoted father and their marriage as a true partnership. “Many working moms feel this way — there is a lot of guilt,” she said. “I don’t think I could do it if I didn’t have the full support system I have, if Anthony wasn’t willing to be, essentially, a full-time dad.”

But the two people close to the couple said Ms. Abedin and Mr. Weiner had been growing apart for some time, with Ms. Abedin often on the campaign trail with Mrs. Clinton and Mr. Weiner at home with Jordan. They said the Post article had not caused a sudden and unexpected rupture to a happy marriage, but rather was the final catalyst for Ms. Abedin to move for a separation.

Campaign officials had braced for new revelations about Mr. Weiner after The Post reported this month that a Republican had baited Mr. Weiner into a flirtatious online chat. Asked by The New York Times this month whether he was still engaging in the behavior that had foiled his political career, Mr. Weiner said, “I’m not going to go down the path of talking about any of that.”

Mrs. Clinton had hoped to ride out the final week of August with limited distractions as she seeks to maintain her solid lead in national polls. On Monday, she attended three fund-raisers in the Hamptons, without Ms. Abedin, and spoke briefly on a conference call with policy experts and medical providers to unveil her proposals on mental health.

“We’ve got to make clear mental health is not a personal failing,” Mrs. Clinton said.

Aides said that Ms. Abedin’s marriage was a private matter and that her decision to announce the separation meant the frenetic news cycle would soon move on.